Dependence of the aeroelastic stability of a slender U-beam on the realized flow pattern

We investigate the aeroelastic behaviour of a slender U-beam in cross-flow. Two distinct, time periodic flow patterns are observed in simulations of the flow around this beam. Its aeroelastic properties depend on the realized flow pattern, especially so for low reduced velocities: One flow pattern leads to pronounced torsional vortex-induced vibrations. No such vibrations could be observed under the other flow pattern. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Nonlinear vibrations of piezoelectric microcantilevers for biologically-induced surface stress sensing

In this paper, nonlinear vibrations of a piezoelectrically-driven microcantilever beam in presence of a biological monolayer are investigated and the corresponding equations of motion are derived and simulated. A part of the microcantilever beam surface is covered by a piezoelectric layer, which acts as an actuator. Inextensibility condition and the coupling between electrical and mechanical properties in piezoelectric materials are considered in the bending vibrations of the beam. The adsorbed biological layer is considered to be a monolayer and its adsorption induced surface stress is formulated from the molecular viewpoint. The nonlinear terms in the governing equations of motion of the beam appear in the quadratic form due to the presence of the piezoelectric layer, and the cubic form due to geometry of the beam and the adsorbed biological layer. Through extensive numerical simulations, it is demonstrated that the nonlinear effect of piezoelectric layer is significant in the microcantilever resonance sensing range. It is also shown that the effect of intermolecular attraction–repulsion on the surface stress is less dominant than other sources of surface stress (e.g., the electrostatic forces). Finally, it is observed that piezoelectrically-actuated microcantilever provides the ability of indirect measurement of vibrations and frequency response characteristics, instead of using bulky laser sensor.     

Effect of Torsion and Warping on the Free Vibration of Sandwich Beams

The problem on free vibrations of wide sandwich beams is tackled in this paper. Torsional and warping effects in addition to flexure are included in the formulation of the dynamic problem. In order to show the effects of bending-torsion coupling and warping on the natural frequencies and the corresponding vibration modes, three cases are considered. First, the warping and torsion effects are neglected, second, the effect of warping on the coupling terms is neglected, and third, the effect of warping on the coupling terms is included. The viscoelastic core is modeled by elastic translational and rotational springs. The finite-difference method is used to solve the partial differential equations of motion with different boundary conditions for the top and bottom layers. Results for different materials, fiber orientations, depth-to-width ratios, and boundary conditions are found. The natural frequencies and the corresponding vibration modes obtained are in a good agreement with those cited in the literature. If the bending-torsion coupling is pronounced, the inclusion of warping affects the natural frequency considerably.__________Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 41, No. 2, pp. 163–176, April–May, 2005.     

Control-oriented Rotordynamics

The rotor vibrations are coupled by many parameters: angular speed couples two radial directions, unbalance couples torsional and lateral vibrations, rotor support couples rigid body and flexible modes. Small changes of these parameters strongly influence the rotor dynamics. The full analysis of the rotor coupled vibrations is much simpler when we can divide the system into smaller subsystems. In this case the calculations are simplified and we have deep insight into mechanisms leading to good or bed behaviour of the rotor motion. It is particularly important in the case of the rotor working in the wide range of the angular speeds. For the vibration analysis the methods known from control theory can be applied. The proposed approach was testified in the paper on the simple 3-mode rotor model. The torsional vibrations were separated from the lateral vibrations and a feedback among the subsystems was established. The subsystems are coupled by rotor unbalance and root locus method allows to show the critical values of the unbalance which destabilize rotor motion for different angular speeds. The lateral vibrations are stabilized by angular speed and again it is possible to find how big value of the rotor speed is sufficient to stabilize the rotor motion. Such analysis of the rotor vibrations appeared very useful for the choice of the control strategy. It indicated such control laws which amplify the stabilizing mechanisms in the rotor dynamics. Such procedures can also lead to the energy saving control laws. In the case of the lateral vibrations there were considered four control strategies. And these strategies were compared to indicate optimal one. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

两自由度非对称三次系统非线性模态的奇异性质

利用非线性模态子空间的不变性和摄动技术,研究两自由度非对称三次系统在奇异条件下系统的性质.重点考虑子系统之间线性耦合退化时的奇异性质.对于非共振情形,所得到的解析结果表明,系统出现单模态运动以及振动局部化现象,这种现象的强弱不但与非线性耦合刚度有关,而且与非对称参数有关.并解析地得到了参数的门槛值;对于1:1共振情形,模态随非线性耦合刚度和非对称参数的变化会出现分岔,得到了参数分岔集以及模态的分岔曲线.     

Finite element approximation of coupled seismic and electromagnetic waves in fluid‐saturated poroviscoelastic media

This work presents a collection of global and iterative finite element procedures for the numerical approximation of coupled seismic and electromagnetic waves in 2D bounded fluid‐saturated porous media, with absorbing boundary conditions at the artificial boundaries. The equations being analyzed are the coupled Biot's equations of motion and Maxwell equations in the diffusive range. Both seismoelectric and electroseismic coupling are simultaneously included and analyzed in the model. The case of compressional and vertically polarized shear waves coupled with the transverse magnetic polarization (PSVTM‐mode) is analyzed in detail, including the derivation of a priori error estimates on the global finite element procedure and results on the convergence of a domain decomposition iterative algorithm. Later, the corresponding results for the case of horizontally polarized shear waves coupled with the transverse electric polarization (SHTE‐mode) are stated. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2011     

A parametric investigation of the harmonic vibrations of a poroelastic rod

The problems of calculating the forced harmonic vibrations of porous structures saturated with a fluid are considered. The equations of motion are obtained by starting from general relations of the Biot theory of poroelasticity and continuous mechanics after taking into account the anisotropy of the elastic and hydraulic properties of the medium. The influence of the mechanical constants of the material on its dynamical characteristics is investigated using the example of the flexural vibrations of a simple rod-shaped structure.     

Vibrations of a cylinder in a concentric vessel filled with a two-layer fluid

A hybrid vibrational system containing a solid (a cylinder) with an elastic connection to a coaxial cylindrical cavity, completely filled with a heavy ideal stably stratified two-layer fluid, is considered. The combined self-consistent vibrations of the body and the fluid (of the internal waves) are studied. An explicit solution of the internal boundary value problem of an inhomogeneous liquid in an annular domain for a specified motion of the body is obtained. An integrodifferential equation of the Newton type is constructed on the basis of this. This equation describes the self-consistent oscillations of the cylinder. In the case of weak coupling of the interaction between the solid and the medium, an approximate solution is obtained using asymptotic methods and an analysis is carried out. Qualitative effects of the mutual effect of the motions of the cylinder and the fluid are found.     

Numerical modeling of the active damping of forced thermomechanical resonance vibrations of viscoelastic shells of revolution with the help of piezoelectric inclusions

We consider the problem of active damping of forced resonance vibrations of viscoelastic shells of revolution with the help of piezoelectric sensors and actuators. Here, the interaction of electromechanical and thermal fields is taken into account. For modeling of vibrations, we use the Kirchhoff–Love hypotheses as well as hypotheses adequate to them and describing the distribution of temperature and electric field quantities. The shell temperature increases as a result of dissipative heating. For the active damping of vibrations, piezoelectric sensors and actuators are used. It is supposed that the electromechanical characteristics of materials depend on the temperature. The solution of this complex nonlinear problem has been obtained by the iterative method and finite element method. We have investigated the influence of temperature of dissipative heating on the efficiency of active damping of vibrations of a viscoelastic cylindrical panel with rigid restraint of its edges.     

Relation between the mechanical properties of polymers and the kinetic flexibility of the macromolecules

Nuclear magnetic resonance combined with extension of the specimens in the NMR spectrometer on the reversible deformation range has been used to study the cooperative modes of motion of the macromolecules in polymers, specifically polycaprolactam and polyethylene terephthalate. For each of these polymers there are two temperatures near which the nature of the molecular motion changes sharply. At low temperatures there is a transition from independent hindered vibrations of the repeating units to correlated vibrations, as a result of which the chains in the amorphous regions acquire limited kinetic flexibility within the glassy state; at high temperatures there is a transition to segmental motion. The question of how changes in the modes of molecular motion are reflected in the macroscopic mechanical properties of polymers is examined.Ioffe Physicotechnical Institute, Academy of Sciences of the USSR, Leningrad. Translated from Mekhanika Polimerov, No. 1, pp. 24–29, January–February, 1971.     

Effect of an elastic core on the dynamic stability of an orthotropic cylindrical shell

A method of determining the regions of dynamic instability of an orthotropic cylindrical shell "bonded" to an elastic cylinder is proposed. An expression for the core reaction is obtained from the coupling conditions for the forces normal to the lateral surface and the radial displacements of the shell and the core at the contact surface. When the reaction is substituted in the system of equations of motion of the shell, the part corresponding to the free vibrations of the cylinder is discarded. The system of equations of motion of the shell is reduced to an equation of Mathieu type, from which transcendental equations for determining the boundaries of the regions of dynamic instability are obtained. These regions are analyzed for various modes of loss of stability and different values of the core modulus of elasticity.     

2D simulation of fluid-structure interaction using finite element method

This paper deals with pressure-based finite element analysis of fluid–structure systems considering the coupled fluid and structural dynamics. The present method uses two-dimensional fluid elements and structural line elements for the numerical simulation of the problem. The equations of motion of the fluid, considered inviscid and compressible, are expressed in terms of the pressure variable alone. The solution of the coupled system is accomplished by solving the two systems separately with the interaction effects at the fluid–solid interface enforced by an iterative scheme. Non-divergent pressure and displacement are obtained simultaneously through iterations. The Galerkin weighted residual method-based FE formulation and the iterative solution procedure are explained in detail followed by some numerical examples. Numerical results are compared with the existing solutions to validate the code for sloshing with fluid–structure coupling.     

Vibrations and stability of axially traveling laminated beams

In this paper, vibrations and stability of an axially traveling laminated composite beam are investigated analytically via the method of multiple scales. Based on classical laminated beam theory, the governing equations of motion for a time-variant axial speed are obtained using Newton’s second law of motion and constitutive relations. The method of multiple scales, an approximate analytical method, is applied directly to the gyroscopic governing equations of motion and complex eigenfunctions and natural frequencies of the system are obtained. The stability boundaries of the system near resonance are determined via the Routh-Hurwitz criterion. Finally, a parametric study is conducted which considers the effects of laminate type and configuration as well as the mean speed and amplitude of speed fluctuations on the vibration response, natural frequencies and stability boundaries of the system.     

The dual nature of the transverse vibrations of an elastic rod

The transverse vibrations of an elastic rod, to one of which displacements are applied while the other end is free, are investigated. It is assumed that the propagation velocity of the perturbations in the rod is finite. The unperturbed part performed rotational motion around the centre line. The angle of rotation is expressed by the angle of curvature of the centre line of the perturbed part of the rod. Two types of elastic vibrations are obtained: (1) the rod vibrates elastically due to displacements applied at the end, and (2) when performing rotational motion elastic vibrations and additional forces occur in the rod due to elasticity [1].     

FSI of a Simplified Aero Engine Compressor Cascade Configuration

A first approach of fully coupled computations of blade vibrations in a two dimensional compressor cascade configuration will be presented in this article. The simulations are realised applying an explicit, partitioned coupling approach between established CFD- and FEM-codes. Investigations are focussed on numerical effects and behaviour on blade vibrations such as damping and frequency shift dependent on inviscid, subsonic flow parameters. The theoretical background, modelling steps and computational results of numerical experiments are discussed. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Nonlinear vibrations of a ropeway system with moving passenger cabins

The dynamic continuous model of a carrying rope for circulating bicable aerial ropeway is formulated. To describe nonlinear in-plane vibrations excited by moving masses of passenger cabins a closed form model with Green-Lagrange deformation is developed. The equations of motion of the system are derived on the basis of Lagrange equations with Ritz approximation of cable displacements applied. Numerical example of linear and nonlinear cable vibrations is presented. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Coupling Techniques for Thermal and Mechanical Fluid-Structure-Interactions in Aeronautics

For the coupled thermal and mechanical analysis of spacecraft structures a simulation environment was developed containing the necessary coupling techniques. The numerical concept uses the weak form of the interface conditions on the coupling surface. The iterative solution of the coupled equations is based on the classical Dirichlet-Neumann approach. Transient problems are handled with iterative staggered schemes. A flexible component-based software environment combines existing fluid and structural analysis codes. Aspects of the architecture and its implementation are described. Finally an application to a spacecraft structure is shown. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Study of non-linear dynamic behavior of open cracked functionally graded Timoshenko beam under forced excitation using harmonic balance method in conjunction with an iterative technique

The nonlinear modeling and subsequent dynamic analysis of cracked Timoshenko beams with functionally graded material (FGM) properties is investigated for the first time using harmonic balance method followed by an iterative technique. Crack is assumed to be open throughout. During modeling, nonlinear strain–displacement relation is considered. Rotational spring model is adopted in order to model the open cracks. Energy formulations are established using Timoshenko beam theory. Nonlinear governing differential equations of motion are derived using Lagrange's equation. In order to incorporate the influence of higher order harmonics, harmonic balance method is employed. This reduces the governing differential equations into nonlinear set of algebraic equations. These equations are solved using two different iterative techniques. Methodology is computationally easier and efficient as well. This is observed that although assumption of simple harmonic motion (SHM) simplifies the problem, it yields to erroneous results at higher amplitude of motion. However, accuracy of the solution is improved considerably when the contribution of higher order harmonic terms are considered in the analysis. Results are compared with the available results, which confirm the validity of the methodology. Subsequent to that a parametric study on influence of forcing term, material indices and crack parameters on large amplitude vibration of Timoshenko beams is performed for two different boundary conditions.